[Paper Review] An efficient classification in IBE Provide with an improvement of BB2 to an efficient Commutative Blinding scheme

Rkia Aouinatou, Mostafa Belkasmi|arXiv (Cornell University)|Aug 6, 2012

Cryptography and Data Security29 references3 citations

TL;DR

This paper proposes an improved commutative blinding scheme based on the BB2 identity-based encryption (IBE) framework, enhancing efficiency and security by leveraging a strong Diffie-Hellman problem. The scheme achieves constant-size ciphertexts and supports selective-ID+ security with identities in $\mathbb{Z}_p$ rather than $\mathbb{Z}_p^*$, offering better flexibility and performance than prior HIBE constructions like BBG.

ABSTRACT

Because of the revolution and the success of the technique IBE (Identification Based Encryption) in the recent years. The need is growing to have a standardization to this technology to streamline communication based on it. But this requires a thorough study to extract the strength and weakness of the most recognized cryptosystems. Our first goal in this work is to approach to this standardization, by applying a study which permit to extract the best cryptosystems. As we will see in this work and as Boneh and Boyen said in 2011 (Journal of Cryptology) the BB1 and BB2 are the most efficient schemes in the model selective ID and without random oracle (they are the only schemes traced in this model). This is right as those schemes are secure (under this model), efficient and useful for some applications. Our second goal behind this work is to make an approvement in BB2 to admit a more efficient schemes. We will study the security of our schemes, which is basing on an efficient strong Diffie-Hellman problem compared to BB1 and BB2. More than that our HIBE support s+ID-HIBE compared to BBG (Boneh Boyen Goh). Additionally the ID in our scheme will be in Zp instead of Zp* as with BBG. We will cite more clearly all these statements in in this article.

Motivation & Objective

• To address the need for standardization in identity-based encryption (IBE) by identifying and improving upon the most efficient and secure IBE schemes.
• To enhance the BB2 IBE scheme by introducing a more efficient commutative blinding mechanism based on a strong Diffie-Hellman problem.
• To support hierarchical IBE (HIBE) with $s^+$-ID security and reduce identity constraints by using $\mathbb{Z}_p$ instead of $\mathbb{Z}_p^*$ for identities.
• To improve efficiency and security in HIBE by minimizing ciphertext size and decryption cost, independent of hierarchy depth.
• To provide a practical, secure, and standardized IBE framework suitable for real-world deployment.

Proposed method

• The scheme extends the BB2 IBE construction using a commutative blinding technique to improve efficiency and security.
• It introduces a new security model based on the strong Diffie-Hellman problem, strengthening security compared to BB1 and BB2.
• The identity space is redefined from $\mathbb{Z}_p^*$ to $\mathbb{Z}_p$, enabling broader identity selection and simplifying implementation.
• The scheme maintains constant-size ciphertexts (three group elements) and two bilinear pairing operations in decryption, independent of hierarchy depth.
• Security is proven in the selective-ID+ model, ensuring resistance to chosen-identity attacks with full simulation security.
• The construction integrates techniques from Boneh-Boyen-Goh (BBG) but improves upon their identity constraints and efficiency.

Experimental results

Research questions

• RQ1 How can the BB2 IBE scheme be enhanced to achieve better efficiency and stronger security without relying on random oracles?
• RQ2 Can a commutative blinding scheme be designed to support $\mathbb{Z}_p$ identities instead of $\mathbb{Z}_p^*$, improving flexibility and performance?
• RQ3 What is the impact of using a strong Diffie-Hellman problem on the security and efficiency of IBE and HIBE constructions?
• RQ4 To what extent can ciphertext size and decryption cost be minimized in hierarchical IBE while maintaining security?
• RQ5 How does the proposed scheme compare to BBG and other HIBE schemes in terms of security model, efficiency, and identity representation?

Key findings

• The proposed scheme achieves constant-size ciphertexts of three group elements, matching the efficiency of BBG and BB2.
• Decryption requires only two bilinear pairing operations, independent of the hierarchy depth, significantly improving performance.
• The scheme supports $s^+$-ID security, a stronger model than selective-ID, with a security reduction factor of $N \geq 2^{160}$.
• By using $\mathbb{Z}_p$ instead of $\mathbb{Z}_p^*$ for identities, the scheme removes the need for multiplicative inverses, simplifying implementation and increasing identity flexibility.
• The security of the scheme is based on a strong Diffie-Hellman problem, which is more robust than the decisional problems used in BB1 and BB2.
• The scheme outperforms BBG in terms of identity representation and efficiency, while maintaining comparable security and performance characteristics.